Let $f, g : [a, b] \to \mathbb{R}$ each be a D1760: Riemann integrable real function such that

(i)	\begin{equation} f \leq g \end{equation}

Then \begin{equation} \int^b_a f(x) \, d x \leq \int^b_a g(x) \, d x \end{equation}

Let $f, g : [a, b] \to \mathbb{R}$ each be a D1760: Riemann integrable real function.

Then \begin{equation} f \leq g \quad \implies \quad \int^b_a f(x) \, d x \leq \int^b_a g(x) \, d x \end{equation}

Let $f, g : [a, b] \to \mathbb{R}$ each be a D1760: Riemann integrable real function such that

(i)	\begin{equation} \forall \, x \in [a, b] : f(x) \leq g(x) \end{equation}

Then \begin{equation} \int^b_a f(x) \, d x \leq \int^b_a g(x) \, d x \end{equation}